Noncommutative geometry and applications

这个建议包括两个项目，计划在各种几何背景下使用非交换几何。项目#1：非对易几何，CR几何和费曼程序。本项目的总目标是利用非交换几何和伪微分技术，将Kohn-Rossi复形的亚椭圆分析与基础流形的CR微分几何联系起来。它包括三个项目。第一个项目旨在重新制定CR几何中的局部指数公式，第二个项目计划给出Kohn-Rossi复体的欧拉特征的几何表达式，最后一个项目涉及CR几何中February man程序的应用。项目#3：非对易几何中的高指数公式和量子霍尔效应。本项目旨在证明Connes-Moscovici非对易几何中局部指数公式的“更高”版本。这在一定程度上是由与Mathai Varghese关于量子霍尔效应的联合项目推动的。

This proposal consists of two items which plans to make use of noncommutative geometry in various geometric contexts.- Item #1: Noncommutative geometry, CR geometry and Fefferman's program. The general aim of this item  to make use of noncommutative geometry and of pseudodifferential techniques to relate the hypoelliptic analysis of the Kohn-Rossi complex to the CR differential geometry of the underlying manifold. It consists of 3 projects. The first project aims to reformulate the local index formula in CR geometry, the second one plans to give a geometric expression for the Euler characteristic of the Kohn-Rossi complex and the last one concerns applications to Fefferman's program in CR geometry.- Item #3: Higher index formula in noncommutative geometry and the quantum Hall effect. This item aims to prove ``higher'' versions of the local index formula in noncommutative geometry of Connes-Moscovici. This is partly motivated by a joint project with Mathai Varghese about the quantum Hall effect.